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N. A. Slavnov

Publications and source records attributed to N. A. Slavnov.

70 records · Page 4Linked to original sources
arXiv2004

Master equation for spin-spin correlation functions of the XXZ chain

We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the one hand to the previously obtained multiple integral formulas for the spin-spin correlation functions and on the other hand to their expansion in terms of the form factors of the local spin operators. Hence, it provides a direct analytic link between these two representations of the correlation functions and a complete re-summation of the corresponding series. The master equation method also allows one to obtain multiple integral representations for dynamical correlation functions.

hep-th↗
arXiv2002

Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field

Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field. At lattice distance m, they are typically given as the sum of m terms. Each term n of this sum, n = 1,...,m is represented in the thermodynamic limit as a multiple integral of order 2n+1; the integrand depends on the distance as the power m of some simple function. The root of these results is the derivation of a compact formula for the multiple action on a general quantum state of the chain of transfer matrix operators for arbitrary values of their spectral parameters.

hep-th↗
arXiv1998

Integral equations for the correlation functions of the quantum one-dimensional Bose gas

The large time and long distance behavior of the temperature correlation functions of the quantum one-dimensional Bose gas is considered. We obtain integral equations, which solutions describe the asymptotics. These equations are closely related to the thermodynamic Bethe Ansatz equations. In the low temperature limit the solutions of these equations are given in terms of observables of the model.

solv-int↗
arXiv1998

The form factors in the finite volume

The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.

math-ph↗
arXiv1998

On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case

We consider the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant. This correlation function admits a Fredholm determinant representation. The related operator-valued Riemann--Hilbert problem is used for analysing the leading term of the large time and long distance asymptotics of the correlation function.

math-ph↗
arXiv1998

The determinant representation for quantum correlation functions of the sinh-Gordon model

We consider the quantum sinh-Gordon model in this paper. Using known formulae for form factors we sum up all their contributions and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only in the theory of correlation functions, but also in the matrix models.

hep-th↗
arXiv1997

Normal Ordering in the Theory of Correlation Functions of Exactly Solvable Models

We study models of quantum statistical mechanics which can be solved by the algebraic Bethe ansatz. The general method of calculation of correlation functions is based on the method of determinant representations. The auxiliary Fock space and auxiliary Bose fields are introduced in order to remove the two body scattering and represent correlation functions as a mean value of a determinant of a Fredholm integral operator; the representation has a simple form for large space and time separations. In this paper we explain how to calculate the mean value in the auxiliary Fock space of asymptotic expression of the Fredholm determinant. It is necessary for the evaluation of the asymptotic form of the physical correlation functions.

hep-th↗
arXiv1997

The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation

We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued Fredholm determinant. In this paper we show that a Riemann-Hilbert problem can be associated with this Fredholm determinant. This Riemann-Hilbert problem formulation permits us to write down completely integrable equations for the Fredholm determinant and to perform an asymptotic analysis for the correlation function.

hep-th↗
arXiv1992

Temperature Correlations of Quantum Spins

Isotropic XY is considered. It describes interaction of quantum spins on 1-dimesional lattice. Alternatevly one can call the model XXO Hiesenberg antiferromagnet. We solved long standing problem of evaluation of temperature corelations. We proved that correlation function of the model is $τ$ function of Ablowitz-Ladik PDE. We explicitly evaluated asymptotics.

hep-th↗